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Revisiting Exhaustivity and Specificity Using Propositional Logic and Lattice Theory
2013
Proceedings of the 2013 Conference on the Theory of Information Retrieval - ICTIR '13
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We use propositional logic and lattice theory in order to redefine the two implications and their uncertainty P (d → q) and P (q → d). ...
Exhaustivity and Specificity in logical Information Retrieval framework were introduced by Nie [16]. ...
We redefine Exhaustivity and Specificity using Propositional Logic and Lattice theory, and we theoretically integrate them into IR models, in Section 3. ...
doi:10.1145/2499178.2499187
dblp:conf/ictir/AbdulahhadCB13
fatcat:vdxgkvcacrcnlpvmrdb7kvuvxu
A Lattice-Based Approach to Computing Warranted Beliefs in Skeptical Argumentation Frameworks
2007
International Joint Conference on Artificial Intelligence
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We show that such search space can be defined as a lattice, and illustrate how the so-called dialectical constraints can play a role for guiding the efficient computation of warranted arguments. ...
This research was partially supported by the Dept. of Computer Science and Eng., SeCyT, U.N.Sur, CONICET, and ANPCyT (PICT 13096, 15043, PAV076), Argentina. ...
Partial research support was also obtained from Project TIN2004-07933-C03-01/03 and Ramón y Cajal Program (MCyT, Spain). ...
dblp:conf/ijcai/ChesnevarS07
fatcat:o7d3kqadwnhtdluipvqyd3wxsa
Computational Complexity of Deciding Provability in Linear Logic and its Fragments
[article]
2021
arXiv
pre-print
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Linear logic has, for example, found applications in proof theory, quantum logic, and the theory of programming languages. ...
This interpretation makes linear logic a useful tool for formalisation in mathematics and computer science. ...
For this, we propose a lattice of fragments of linear logic, inspired by Post's lattice for propositional logic [ ]. ...
arXiv:2110.00562v1
fatcat:a6sidawnbjh5jpf2cvrermfrcy
Logic Column 18: Alternative Logics: A Book Review
[article]
2007
arXiv
pre-print
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This article discusses two books on the topic of alternative logics in science: "Deviant Logic", by Susan Haack, and "Alternative Logics: Do Sciences Need Them?", edited by Paul Weingartner. ...
Here are some (by no means disjoint or exhaustive) categories we can readily identify: • Specification and verification: The problem of specifying and formally verifying properties of systems is central ...
Specification are often expressed in a form of modal logic, and verified by model checking: the logic serves as a formal language for writing down specifications, and verification amounts to checking that ...
arXiv:0705.1367v1
fatcat:sehpdwjpwvbepakwz65tkzokze
The Circus Testing Theory Revisited in Isabelle/HOL
[chapter]
2013
Lecture Notes in Computer Science
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Based on this formal representation of the semantics we revisit the original associated testing theory. We discovered unforeseen simplifications in both definitions and symbolic computations. ...
The approach lends itself to the construction of a tool, that directly uses semantic definitions of the language as well as derived rules of its testing theory, and thus provides some powerful symbolic ...
Isabelle/HOL uses this specification to define the relation as least fixed-point on the lattice of powersets (according to Knaster-Tarski). ...
doi:10.1007/978-3-642-41202-8_10
fatcat:ubmaipwzuje2vcf67myeb7ph3y
A General Theory of Concept Lattice (I): Emergence of General Concept Lattice
[article]
2019
arXiv
pre-print
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It will be shown that one can always regain the formal concept lattice and rough set lattice from the general concept lattice. ...
As the first part of the treatise on A General Theory of Concept Lattice (I-V), this work develops the general concept lattice for the problem concerning categorization of objects according to their properties ...
One may construct the GCL in terms of lattice theory [1, 10, 12] . Proposition 3.16. ...
arXiv:1908.01056v1
fatcat:dqbldxlvdbcnfdvnjc2xn5bew4
Quantum Logical Structures For Identical Particles
[article]
2013
arXiv
pre-print
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In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. ...
In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosoph-ical implications. ...
The standard quantum logical approach to QM [10, 11, 30, 43, 8, 12, 27] , uses the lattice of projections of the Hilbert space of the system as the lattice of propositions (see Section 3) . ...
arXiv:1305.5242v1
fatcat:ccqg5l6k65fqjpcaeqvmtlm7gy
Using SPARQL to Test for Lattices: Application to Quality Assurance in Biomedical Ontologies
[chapter]
2010
Lecture Notes in Computer Science
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Our experimental results have been groundbreaking: for the first time, all non-lattice pairs in SNOMED CT have been identified exhaustively from 34 million candidate pairs using over 2.5 billion queries ...
RDF, SPARQL and related tooling provide an eAEcient platform for implementing lattice algorithms on large data structures. ...
Acknowledgements This research was supported in part by the Intramural Research Program of the National Library of Medicine (NLM), and in part by Clinical and Translational Science Award (UL1 RR024989) ...
doi:10.1007/978-3-642-17749-1_18
pmid:25699294
pmcid:PMC4330995
fatcat:srdrq2xsmff53bgw3cmugzbyxe
Relevant Logic and Paraconsistency
[chapter]
2005
Lecture Notes in Computer Science
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The relevant refusal to validate these inferences is defended, and finally it is suggested that more needs to be done towards a satisfactory theory of when they may nonetheless safely be used. ...
The relationship between relevant logic and resolution, and especially the disjunctive syllogism, is then examined. ...
Suppose that truth and falsehood are neither collectively exhaustive nor mutually exclusive, but rather are treated in the formal semantics of logic as two independent properties that propositions may ...
doi:10.1007/978-3-540-30597-2_9
fatcat:552ct22xdbahzkksi4c67tnkhe
A method for rigorous design of reconfigurable systems
2016
Science of Computer Programming
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The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic ...
This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation ...
Examples range from classical logics (propositional, equational, first order, etc.), to the ones underlying specification and programming languages or used for describing particular systems from different ...
doi:10.1016/j.scico.2016.05.001
fatcat:eqtbwavwqfgihmcyuls3vq73oy
An Algebraic Glimpse at Bunched Implications and Separation Logic
[article]
2018
arXiv
pre-print
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We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics. ...
After briefly discussing the lattice of subvarieties of GBI, we present a suitable duality for GBI along the lines of Esakia and Priestley and an algebraic proof of cut elimination in the setting of residuated ...
other things would not have happened; Nick Galatos and Kazushige Terui for suggesting the idea to write this overview, and for their patience and support during the very long write-up period; Nick, Peter ...
arXiv:1709.07063v2
fatcat:mo56tyegqned5htws2wazhpphu
Topological duality for distributive lattices, and applications
[article]
2022
arXiv
pre-print
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: semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata. ...
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. ...
: semantics of propositional logics, domain theory in logical form, and the theory of profinite monoids for the study of regular languages and automata. ...
arXiv:2203.03286v2
fatcat:bs6pfodmkfgnhpegiuvcymb3fy
Truth versus information in logic programming
2013
Theory and Practice of Logic Programming
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This allows us to shed new light on many aspects of logic programming, including program analysis, type and mode systems, declarative debugging and the relationships between specifications and programs ...
In this paper we suggest that the additional truth values of Fitting/Kunen and Naish are best viewed as duals. We use Belnap's four-valued logic (Belnap, N. D. 1977. A useful four-valued logic. ...
Two-valued semantics There are three aspects to the semantics of logic programs: proof theory, model theory and fixed point theory (see Lloyd (1984) , for example). ...
doi:10.1017/s1471068413000069
fatcat:iud5qwdojrdqvl6qiu45pl5oym
Formal Concept Analysis and Information Retrieval – A Survey
[chapter]
2015
Lecture Notes in Computer Science
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Currently, FCA theory supports dozens of different retrieval applications, ranging from traditional document indices to file systems, recommendation, multi-media and more recently, semantic linked data ...
In this paper we present a comprehensive study on how FCA has been used to support IR systems. ...
How have FCA and concept lattices been used in the context of IR applications? ...
doi:10.1007/978-3-319-19545-2_4
fatcat:ibbabj5khbecrj3zgvmalpb6ja
Logic for physical space
2011
Synthese
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From the initial axiomatic efforts of Euclid, we revisit the major milestones in the logical representation of space and investigate current trends. ...
This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. ...
Acknowledgements We thank Elisabetta Pallante for fruitful discussion on the theory of quantum gravity and de Sitter space-time. ...
doi:10.1007/s11229-011-9913-9
fatcat:agtphwjsufexvpxrwbpzkqjotq
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